Question

cos(tan^-1(sqrt 3))
Need help!!!

Answer 1

what u need help with

Answer 2

I don't really understand how to work the problem above.

Answer 3

Remember that tangent is sine over cosine.
This means one fraction divided by another will give √(3)
When you divide a fraction by a fraction, you flip the second fraction.
Since the result is √(3), you know that √(3) is in the numerator of the problem.

That indicates the use of √(3)/2 as the first value. It indicates the first one because if it were the second one, it would be flipped and become 1/√(3). Since tangent is sine over cosine, think of when sine is √(3)/2:

sin( π/3 ) = sin( 60° ) = √(3)/2

And cosine there is:
cos( π/3 ) = cos( 60° ) = 1/2

Thus tangent is:
tan( π/3 ) = tan( 60° )
= sin( 60° )/cos( 60° )
= [ √(3)/2 ] / [ 1/2 ]
= [ √(3)/2 ] × [ 2/1 ]
= [ √(3)/1 ] × [ 1/1 ]
= √(3)

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The exact value is π/3 radians or 60°.

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If you need arctangent of 1/√(3) then you would know that the flipped fraction had √(3) and look for when cosine is √(3)/2.

Answer 4

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